# prob 6 - Mathematical Expectations Dr.Bimal Kumar Mishra...

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Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii Mathematical Expectations

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Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii Expected value Let (X , Y )be two dimensional random variable with joint density f XY. Let H(X,Y) be a random variable. The expected value of H(X,Y) , denoted by E[H(X,Y) ] is given by 1. E[H(X,Y) ] = ( ) ∑∑ x all y all XY y x f y x H ) , ( ,
Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii provided exists for (X , Y ) discrete; 2. E[H(X,Y) ] = provided exists for (X , Y ) continuous; ( ) - - dydx y x f y x H XY ) , ( , ( ) - - dydx y x f y x H XY ) , ( , ( ) ∑∑ x all y all XY y x f y x H ) , ( ,

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Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii Univariate averages Found Via the Joint Density E[X]= for (X , Y ) discrete E[Y]= ∑∑ x all y all XY y x xf ) , ( ∑∑ x all y all XY y x yf ) , (
Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii Univariate averages Found Via the Joint Density E[X]= for (X , Y ) continuous E[Y]= - - dydx y x xf XY ) , ( - - dydx y x yf XY ) , (

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Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii Covariance Let (X , Y )be random variables with means μ X and μ Y respectively. The covariance between X and Y, denoted by Cov(X,Y) or σ XY is given by Cov(X,Y)=E[(X- μ X )(Y- μ Y )]
Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii

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